210 LearnersLast updated on May 26th, 2025
Factors of 123
Factors of any number are the dividers or multipliers that can divide the number fully and can be multiplied together to produce the given product, 123. Do you know, factors form the basic approach to solve some general mathematical procedures? This article will give you the insights of factors of 123.
What are the Factors of 123?
The factors of 123 or the numbers which divide 123 exactly are:
1,3,41, and 123.
|
Negative factors of 123 |
-1,-3,-41,-123 |
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Prime factors of 123 |
3,41 |
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Prime factorization of 123 |
3×41 |
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The sum of factors of 123 |
1+3+41+123 = 168 |
How to Find the Factors of 123
For finding factors of 123, we will be learning these below-mentioned methods:
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
- Factor Tree
Finding Factors using Multiplication Methods
This particular method often finds the pair of factors which, on multiplication together, produces 123. Let us find the pairs which, on multiplication, yields 123.
- 1×123=123
- 3×41=123
So, factors of 123 are: 1,3,41, and 123.
Finding Factors using Division Method
The division method finds the factors that evenly divides the given number 123. In this process, we have to divide 123 by all possible natural numbers less than 123 and check.
1,3,41, and 123 are the only factors that the number 123 has. So to verify the factors of 123 using the division method, we just need to divide 123 by each factor.
123/1 =123
123/3=41
123/41=3
123/123=1
Prime Factors and Prime Factorization
Prime Factorization is the easiest process to find prime factors. It decomposes 123 into a product of its prime integers.
- Prime Factors of 123: 3,41.
- Prime Factorization of 123: 3×41
Factor tree
The number 123 is written on top and two branches are extended.
Fill in those branches with a factor pair of the number above, i.e., 123.
Continue this process until each branch ends with a prime factor (number).
The first two branches of the factor tree of 123 are 3 and 41.
Factor Pairs
Positive pair factors: (1,123), (3,41).
Negative pair factors: (-1,-123), (-3,-41).
Common Mistakes and How to Avoid Them in Factors of 123
Solving problems based on factors can, sometimes, lead to misconceptions among children. Let us check what are the common errors are and how to avoid them.
Mistake 1
Factors might be larger than the given number.
Factors can never be larger than the given number, but multiples can be. You need to understand the concept that factors are integers which divide a given number perfectly, and multiples are the products we get when the original number is multiplied with different numbers.
Factors of 123 Examples
Problem 1
The LCM of two numbers is 123 and their GCF is 1. If one of the numbers is 41, find the other.
We know that the product of two numbers is equal to the product of their GCF and LCM.
⇒ 41× x = 123×1
⇒ x =(123×1) / 41
⇒ x = 3
Answer: The other number is 3.
Explanation
Using the concept of the product of two numbers being equal to the product of their GCF and LCM, we solved it.
Problem 2
Find the simplest form of square root of 123.
√123 = √(123×1) = √123
Answer: The simplest form of square root of 123 is √123.
Explanation
Break down 123 into its product of its prime factor and find its square root by grouping a pair of factors at a time, leaving the remaining single factors under radical.
Problem 3
Find the factors of 246.
The factors of 246 are 1,2,3,6,41,82,123 and 246.
Answer: 1,2,3,6,41,82,123 and 246
Explanation
Found the factors of 246 through division and checking.
Problem 4
Find the smallest number that is divisible by 123 and 246.
Prime factorization of 123: 3×41.
Prime factorization of 246: 2×3×41
LCM of 123 and 246: 2×3×41 = 246
Answer: 246 is the smallest number which is divisible by 123 and 246.
Explanation
To find the smallest number which is divisible by 123 and 246, we need to find the LCM of these numbers.
Problem 5
If a number is divisible by both 3 and 41, is it divisible by 123?
Yes, any number which is divisible by 3 and 41 is also divisible by 123, since 123 = 3×41
Answer: Yes
Explanation
Any number which is divisible by the factor 3 and factor 41 of 123, then it is also divisible by 123 because 123 is a product of 3 and 41.
FAQs on Factors of 123
1.What is the factor tree of 123?
2.Is 123 a prime factor?
3.Is 123 a factor of 246?
4.Is 123 divisible by 3?
5.Is 123 divisible by 6?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 123?
7.What are some fun ways kids in United Kingdom can practice Factors of 123 with numbers?
8.What role do numbers and Factors of 123 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 123 skills?
Important Glossaries for Factors of 123
- Multipliers - Number which multiplies or a number by which another number is multiplied.
- Dividers - A number that divides.
- Prime Factorization - It involves factoring the number into its prime factors.
- Prime factors - These are the prime numbers which on multiplication together results into the original number whose prime factors are to be obtained.
- Composite numbers - These are numbers having more than two factors.
- Multiple - It is a product of the given number and any other integer.
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About BrightChamps in United Kingdom
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
